Power Sum

Discrete Mathematics Level 5

Find \(\displaystyle \sum_{\{a_{1}, \ldots, a_{k}\} \subseteq \{1, 2, 3, 4, 5\}} \frac{1}{a_{1} \cdots a_{k}}\), where the sum is over all nonempty subsets of of the set \(\{1, 2, 3, 4, 5\}\).